Comparison of Monte Carlo and Boltzmann calculation of electron diffusion to absorbing electrodes

Abstract

Calculations have been made of the effect of absorbing electrodes on a continuous stream of electrons travelling in a gas in a uniform electric field. The effective electron drift and diffusion coefficients become a complex function of position, so that the electron density distribution is no longer given by the solution of the electron continuity equation using the usual equilibrium drift velocity and either the transverse or the longitudinal diffusion coefficients appropriate to the applied electric field and gas pressure. Calculations for a momentum transfer cross-section proportional to electron speed indicate an increase of the average electron energy of about a factor of two at the anode. Predictions using Monte Carlo methods and solutions of the Boltzmann transport equation are in good agreement. Monte Carlo calculations are also applied to predict the influence of absorbing boundaries on the Townsend-Huxley experiment (1974). Predicted current ratios compared with ratios obtained from a solution of the continuity equation lie between ratios obtained using both isotropic and conventional transverse and longitudinal diffusion coefficients.